Question

Find the perimeter of the figure on the right. Use 3.14 for .

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2 yd
2 yd
The perimeter is approximately
(Simplify your answer. Type a whole number or a decimal. Round to the nearest hundredth as needed.)

Answer 1

well, for the perimeter we know those two straight lines are just 2 + 2 = 4 yards, now let's add the circumference of that 270° angle.

`\textit{Arc's Length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=2\\ \theta =270 \end{cases}\implies s=\cfrac{(270)\pi (2)}{180}\implies s=3\pi \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE perimeter} }{2~~ + ~~2~~ + ~~3\pi} \implies 2+2+3(3.14)\implies \text{\LARGE 13.42}~yd`